nLab Connections, Curvature, and Cohomology



\infty-Chern-Weil theory

Differential cohomology

\infty-Lie theory

∞-Lie theory (higher geometry)


Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids



Related topics


\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

This entry is about the book

  • Werner Greub, Stephen Halperin, Ray Vanstone:

    Connections, Curvature, and Cohomology

    Academic Press (1973)

    • Volume 1:

      De Rham Cohomology of Manifolds and Vector Bundles


    • Volume 2:

      Lie groups, principal bundles and characteristic classes


    • Volume 3:

      Lie Algebras, Algebraic Connections and Characteristic Classes


on Chern-Weil theory: principal bundles with connections and their characteristic classes.

Related books are


Volume I

0 Algebraic and analytic preliminaries

1 Basic concepts

II Vector bundles

III Tangent bundle and differential forms

IV Calculus of differential forms

V De Rham cohomology

VI Mapping degree

VII Integration over the fiber

VIII Cohomology of sphere bundles

IX Cohomology of vector bundles

X The Lefschetz class of a manifold

  • Lefschetz isomorphism?

Appendix A The exponential map

Volume II

0 Algebraic and analytic preliminaries

I Lie groups

II Subgroups and homogeneous spaces

III Transformation groups

IV Invariant cohomology

V Bundles with structrue group

VI Principal connections and the Weil homomorphism

VII Linear connections

VIII Characteristic homomorphism for Σ\Sigma-bundles

IX Pontrjagin, Pfaffian, Chern classes

X The Gauss-Bonnet-Chern theorem

Appendix A Characteristic coefficients and the Pfaffian

Volume III

0 Algebraic preliminaries

I Spectral sequences

II Koszul complexes of PP-spaces and PP-algebras

III Koszul complexes of PP-differential algebras

IV Lie algebras and differential spaces

V Cohomology of Lie algebras and Lie groups

VI The Weil algebra

VII Operation of a Lie algebra in a graded differential algebra

VIII Algebraic connections and principal bundles

IX Cohomology of operations and principal bundles

X Subalgebras

XI Homogeneous spaces

XII Operation of a Lie algebra on a pair

Appendix A Characteristic coefficients and the Pfaffian

category: reference

Last revised on July 16, 2022 at 05:53:22. See the history of this page for a list of all contributions to it.